[2022/02/17] Nonstandard finite difference/element methods for the second order elliptic equations

Title : Nonstandard finite difference/element methods for the second order elliptic equations

Time : Feb. 17 (Fri), 2:00 pm - 3:00 pm

Place : 31351A SKKU, Suwon

Speaker : Prof. Dongwook Shin (Ajou Univ.)

Abstract : Various natural and physical phenomena can be described by partial differential equations (PDEs). In order to solve these equations, a number of numerical methods have been introduced and developed.
The finite difference and finite element methods are popular and work very well for the boundary value problems. These methods are simple and easy to implement, but the mass conservation property does not hold.
In this talk, we consider nonstandard finite difference/element methods for the second order elliptic equations. Nonstandard methods such as mixed finite element, Discontinuous Galerkin (DG), hybrid DG and hybrid difference methods are locally conservative and important for certain classes of problems, e.g., Darcy flows in porous media and convection diffusion equations. These methods allow high-order accuracy with high-order approximations. However, convergence rates are influenced by smoothness of the solutions. An adaptive algorithm aims to overcome slow convergence for non-smooth solutions. Here, we introduce two types of reliable, efficient, and fully computable a posteriori error estimators and show their numerical results.